Question

How do you express $185,000,000$ in scientific notation?

Answer 1

Hint: In the scientific notation, a number is expressed in the form of $a\times {{10}^{b}}$, where $a$ is a decimal number lying between one and ten, and $b$ is an integer as the exponent over ten. Therefore, for writing the given number $185,000,000$ in the scientific notation, we have to divide it by ten repeatedly until it becomes equal to $1.85$. The number of times the division is carried out will be equal to the exponent over ten in the scientific notation of the number given in the above question.

Complete step-by-step solution:
The number which is given in the above question is \[185,000,000\].
We know that the general form of the scientific notation of a number is given as $a\times {{10}^{b}}$, where $a$ is a number greater than or equal to one, and less than ten. So we have to divide the given number \[185,000,000\] by ten until it becomes equal to $1.85$. Therefore, we divide and multiply the given number by ${{10}^{8}}$ to get
\[\begin{align}
  & \Rightarrow 185,000,000\times \dfrac{{{10}^{8}}}{{{10}^{8}}} \\
 & \Rightarrow \dfrac{185,000,000}{{{10}^{8}}}\times {{10}^{8}} \\
 & \Rightarrow 1.85\times {{10}^{8}} \\
\end{align}\]
Hence, the given number \[185,000,000\] is expressed in scientific notation as \[1.85\times {{10}^{8}}\].

Note: For writing a given number in the scientific notation, we can count the number of digits of the given number. The exponent over ten will be equal to one less than the number of digits in the given number. Like in this case the number of digits in the number \[185,000,000\] is equal to nine, while the exponent over ten is equal to eight, which is one less than nine.